SN 2025fhm: A central-engine powered Ic-BL supernova associated with X-ray transient EP250304a

Abstract: We present X-ray, optical, and radio follow-up observations of EP250304a, an extragalactic fast X-ray transient (EFXT) discovered by the Einstein Probe. Its X-ray light curve exhibits two broad pulses with comparable peak fluxes within the first $\sim$1~ks, a feature rarely seen among low-luminosity gamma-ray bursts or EFXTs. Optical follow-up observations were carried out using the Korea Microlensing Telescope Network, the Thai Robotic Telescope, the Las Cumbres Observatory 1~m global network, the Gemini Multi-Object Spectrograph on Gemini south telescope, and the Global Supernova Network. The fast-cooling phase (within 3 days) of optical data can be well fitted by a shocked cocoon model. However, during the supernova phase (SN 2025fhm, from 3 to 88 days), the late-time light curve cannot be explained solely by radioactive $<sup>{56}$Ni decay, as demonstrated by a grid of simulations using the one-dimensional Lagrangian radiation hydrodynamics code SNEC, which reveals a significant energy excess at late epochs. To account for this excess, a central engine like a rapidly spinning, highly magnetized neutron star is needed to provide additional energy injection. This model yields a best-fit spin period of $\sim$12.60~ms and magnetic field strength of $\sim 3.52\times10^{15} \rm G$, and it successfully explains both the late-time bolometric light curve and the early X-ray pulse structures. Our results indicate that EP250304a/SN 2025fhm is likely powered by a central magnetar rather than by radioactive decay alone, offering new insights into the energy budget and physical origin of EFXTs and their associated supernovae.